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REFRACTION OF LIGHT
GUPTA CLASSES
For any help contact:
9953168795, 9268789880
Nishant Gupta, D-122, Prashant vihar, Rohini, Delhi-85
Contact: 9953168795, 9268789880
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REFRACTION OF LIGHT
Refraction of light:
1.
The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant whose value depends on
sin i v1  2 1
the nature of the two mediums. This is called as Snell’s law. According to this law,


 2
sin r v 2 1
where 12 is called the refractive index of medium 2 with respect to medium 1.
2.
If the medium 1 is vacuum, then v1 = c and the index of refraction of the medium w.r.t. the vacuum is:  = c/v. It is also
called absolute refractive index of medium.
3.
Because the speed of light is different in different mediums and frequency remains unchanged on passing from one

medium to other, hence wavelength of light gets changed with change in medium. The relation is:  medium  air . Thus,

when a light ray from a rarer medium is refracted into a denser medium, its velocity decreases and wavelength decreases
but the frequency does not change.
4.
For air  = 1.0003 which may be taken as 1. Therefore, when light passes from air into any transparent solid the
refractive index is always > 1.
5.
The value of refractive index depends on nature of medium and wavelength or colour of light.
6.
Refractive index is independent of the angle of incidence.
7.
Refractive index decreases with increase in temperature.
8.
When the medium is same on both sides of a glass slab, then the deviation of the emergent ray is zero. That is the
t sin (i  r )
emergent ray goes parallel to the incident ray and lateral displacement of the emergent ray y =
(where t =
cos r
thickness of slab).
9.
Cauchy's formula : The refractive index of a material depends on the wavelength of light according to the
B
relation:   A  2 (where A and B are constants)

10. If ang and anw, are the refractive indices of glass and water w.r.t. air respectively, then refractive index of glass w.r.t.
a
ng
w
water is: n g  a
nw
Real and apparent depth:
1.
If a beaker is filled with water and a person in air observes an object lying at its bottom, then the object appears raised.
actual depth (d ac )
The apparent depth dap is less than the actual depth tac can be shown that apparent depth (d ap ) 
refractive index ( )
2.
If there is an ink spot at the bottom of a glass slab, it appears to be raised by a distance y  d ac  d ap  d 

d
1
 d1  




where d is the thickness of the glass slab and  is its refractive index.
3.
If a beaker is filled with immissible transparent liquids of refractive indices 1, 2, 3 and individual depth d1, d2, d3
d
d
d
respectively, then the apparent depth of the beaker is found to be: d ap  1  2  3
1  2  3
Nishant Gupta, D-122, Prashant vihar, Rohini, Delhi-85
Contact: 9953168795, 9268789880
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Total internal reflection:
1.
For the phenomenon of total internal reflection to take place, it is necessary that a light ray must travel from a denser
medium to a rarer medium, and the angle of incidence in the denser medium must be greater the critical angle for the
given two media.
2.
The critical angle is that angle of incidence for which the angle of refraction becomes 90°. It is given by:
1
1
1
sin i c  1
 R
If the rarer medium is air or vacuum, then sin i c 

2
D
3.
Critical angle for red light is more than that for blue light.
4.
Critical angle increases with the increase in temperature of the medium.
5.
Critical angle depends on (i) nature of medium, (ii) temperature of medium and (iii) wavelength of light.
6.
Air bubbles in glass appear silvery white due to total internal reflection.
7.
A diver in water at a depth d sees the world outside through a horizontal circle of radius r  d tan i c  d /  2  1
8.
The brilliance of diamond is due to the phenomenon of total internal reflection.
9.
Mirages in deserts are also due to refraction and total internal reflection.
10. The working of optical fibre is based on the phenomenon of total internal reflection.
Optical fiber:
1.
It is a glass fiber through which light is transmitted by total internal reflections from one end to other end
2.
An optical fiber may be between 0.01 mm and 0.002 mm in diameter and may be used in bundles with the same relative
positions at both the ends. It is also called as light pipe.
3.
For working of the optical fiber, the angle of incidence should be according to relation sin i   22  12 , where 1 is the
refractive index of the material used for cladding of the pipe and 2 is the refractive index of the core of the pipe.
4.
Optical fibers are used in the field of communications and computers for transmitting and receiving signals converted
into light pulses. They also have medical uses such as in Endoscopy.
Spherical refracting surface:
1.
A spherical refracting surface is a portion of a refracting medium whose curved surface is a part of a sphere. Convex and
concave spherical refracting surfaces are shown in Fig.
2.
The pole, centre of curvature, radius of curvature, aperture, the principal axis, etc., are defined in the same manner as for
mirrors.
Suppose an object is placed in a medium of refractive index 1. The spherical curved surface (convex or concave)
separates it from another medium of refractive index 2 Then, if u, v and R are respectively the object distance, the
image distance and the radius of curvature of the refracting surface, then the formula for relating u, v and R is:
 2 1  2   1


v
u
R
If the object is placed in the medium of refractive index 2 and the curved surface separates it from medium 1 then the
1  2 1   2


formula is
v
u
R
3.
4.
Nishant Gupta, D-122, Prashant vihar, Rohini, Delhi-85
Contact: 9953168795, 9268789880
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Lenses:
1.
A lens is a piece of transparent refractive medium (such as glass, plastic or liquid) bounded by two surfaces one of which
at least must be spherical.
2.
When a lens is thicker in the middle than at the edges, it is called a convex lens or converging lens. When the lens is
thicker at the edges than in the middle, it is called as concave lens or diverging lens.
3.
A thin lens is one in which the distance between the two surfaces along the principal axis is negligibly small. In case of a
thin lens, distances measured from the poles of the refracting surfaces can be taken as the distances measured from the
optical centre of the lens. Optical centre is a point through which a light ray passes undeviated if the lens is quite thin,
Lens Maker's formula and thin lens formula:
 1
1 1 1
1
   (  1)

f v u
 R1 R 2

 where f = focal length of the thin

lens,  = refractive index of the material of lens with respect to the medium surrounding it, R1 = radius of curvature of
the first surface and R2 = radius of curvature of the second surface.
1. When medium is same on both sides of a lens, then
2. For a plano-convex lens or plano-concave lens,
1 (  1)
The focal length is positive for a plano-convex lens, while it

f
R
is negative for a plano-concave lens.
3. If radii of curvatures of the two surfaces are the same, say R, then f 
R
.
2(  1)
Power & magnification due to a lens:
1. Linear magnification is the ratio of the size of image (I) to the size of the object (O), i.e., m = I/O.
v
fv
f
or m 
or m 
u
f
f u
3. For a real image m is negative and for a virtual image m is positive.
4. The power of a lens P =(1/f) dioptre (D). where f is focal length in metre.
Combination of Lenses:
2. For a thin lens (convex or concave)
m
1. Whenever two lenses are in contact, the reciprocal of effective focal length is equal to the sum of the reciprocals of focal
lengths of the lenses in contact.
1 1
1
 
f f1 f 2
2. The power of the combination of two lenses in contact is equal to the sum of the powers of the individual lenses, i.e.,
P = P1+ P2.
3. If two thin lenses are separated by a small distance d, then the focal length of the combination is:
1 1
1
d
 

f f 1 f 2 f 1f 2
Some more points about lenses:
1. When a lens is kept in a medium other than air, then
 1
1  g
1 
 where m is the refractive index of the
 
 1

fm  m
 R 1 R 2 
medium in which lens is placed.
2. When a lens is placed in a medium for which  is less than that of the lens, its focal length increases and power
decreases- The nature of the lens remains unchanged.
3. When the lens is placed in a medium for which  is equal to that of the lens, the focal length of the lens becomes infinity
and power becomes zero. The lens behaves like a plane glass plate.
Nishant Gupta, D-122, Prashant vihar, Rohini, Delhi-85
Contact: 9953168795, 9268789880
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4. When the lens is placed in a medium for which  is greater than that of the lens, the nature of the lens changes. (Air
bubble in water behaves as a divergent lens.)
5. When a lens of focal length f is cut into two equal halves perpendicular to principal axis, then each part of the lens has a
focal length 2f.
6. When a lens of focal length f is cut into two equal halves parallel to principal axis, then each part has a focal length f.
The intensity of image is decreased.
7. For a real image the distance (d) between convex lens and screen must be greater or equal to 4f.
When d < 4f then there is no real image on screen.
When d = 4f then there is only one positions of the lens for which image of the object on the screen is distinct and clear
When d > 4f then there are two positions of the lens for which the image of the object on the screen is distinct and clear.
In these two positions of lens, the distances of object and image from the lens are interchanged. In this case if size of
image in one position is I1 and in other I2 then size of object (O) is given by O  I1I 2
REFRACTION OF LIGHT Assignment
1.
2.
3.
4.
5.
6.
7.
The refractive index of water with respect to air is
4/3 and the refractive index of glass with respect
to air is 3/2. Then the refractive index of water
with respect to glass is;
(a) 9/8
(b) 8/9
(c) 1/2
(d) 2
If μij represents the refractive index when a light
ray goes from medium i to medium j then the
product μ21 x μ32 x μ43 is equal to:
(a) μ32
(b) μ42
(c) μ31
(d) 1/μ14
The refractive index of a given piece of
transparent quartz is greatest for:
(a) red light
(b) violet light
(c) green light
(d) yellow light
A plane glass slab is kept over various coloured
letters; the letter which appears least raised is:
(a) blue (b) violet
(c) green (d) red
A glass slab ( = 1.5) of thickness 3.0 cm is
placed on an ink spot. A person looks at it from a
distance of 5.0 cm above the ink spot. The
distance of the spot will appear to be:
(a) 2.0 cm (b) 3.5 cm (c) 4.0 cm (d) 5.0 cm
The length of a vertical pole at the surface of a
lake of water ( = 4/3) is 24 cm. Then to an underwater fish just below the water surface the tip of
the pole appears to be:
(a) 18 cm above the surface
(b) 24 cm above the surface
(c) 32 cm above the surface
(d) 36 cm above the surface
An air bubble in a glass slab (μ = 1.5) is 5 cm deep
when viewed from, one face and 2 cm deep, when
viewed from the opposite face. The thickness of
the slab is;
(a) 7.5 cm (b) 10.5 cm (c) 7 cm (d) 10 cm
8.
9.
10.
11.
12.
13.
A bird in air looks at a fish vertically below it and
inside water; h1 is the height of the bird above the
surface of water and h 2 the depth of the fish below
the surface of water. If refractive index of water
with respect to air be μ then the distance of the
fish as observed by the bird is:
(a) h1 + h2
(b) h1 + h2/ μ
(c) μ h1 + h2
(d) μ (h1 + h2)
Critical angle of light passing from glass to air is
minimum for:
(a) red (b) green (c) yellow (d) violet
The refractive index of water is 4/3 and that of
glass is 5/3. Then the critical angle for a ray of
light entering water from glass will be:
(a) sin-1 (4/5)
(b) sin-1 (5/4)
-1
(c) sin (20/9)
(d) sin-1 (9/20)
A diver in a swimming pool wants to signal his
distress to a person lying on the edge of the pool
by flashing his waterproof flash light:
(a) he must direct the beam vertically upwards
(b) he has to direct the beam horizontally
(c) he has to direct the beam at an angle to the
vertical which is slightly less than the critical
angle of incidence for total internal reflection
(d) he has to direct the beam at an angle to the
vertical which is slightly more than the
critical angle of incidence for total internal
reflection
The critical angle for light going from medium x
into medium y is θ. The speed of light in medium
x is v. The speed of light in medium y is:
(a) v(l - cos θ)
(b) v/sin θ
(c) v/cos θ
(d) v cos θ
A point source of light is placed 4 m below the
surface of water of refractive index 5/3. The
Nishant Gupta, D-122, Prashant vihar, Rohini, Delhi-85
Contact: 9953168795, 9268789880
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14.
15.
16.
17.
18.
19.
20.
21.
minimum diameter of a disc, which should be
placed over the source, on the surface of water to
cut off all light coming out of water is:
(a) 1 m
(b) 4 m
(c) 3 m
(d) 6 m
A thin convergent glass lens (g = 1.5) has a
power of +5.0. When this lens is immersed in a
liquid of refractive index l it acts as a divergent
lens of focal length 100 cm. The value of l is
(a) 4/3
(b) 5/3
(c) 5/4
(d) 6/5
A double convex lens of focal length 6 cm is made
of glass of refractive index 1.5. The radius of
curvature of one surface is double that of the other
surface. The value of smaller radius of curvature
is:
(a) 6 cm (b) 4.5 cm (c) 9 cm (d) 4 cm
To obtain magnified virtual image of an object by
a convex lens of focal length f, the distance
between the object and the lens should be:
(a) > 4f (b) between 2f and 4f (c) < f (d) >6f
A thin lens has focal length f and its aperture has
diameter d. It forms an image of intensity I, Now,
the central part of the aperture up to diameter (d/2)
is blocked by an opaque paper. The focal length
and image intensity will change to:
(b) (f/2) and (I/2)
(b) f and (I/4)
(c) (3f/4) and (I/2) (d) f and (3I/4)
Diameter of a plano-convex lens is 6 cm and
thickness at the centre is 3 mm. If the speed of
light in the material of the lens is 2 x 108 m/s, the
focal length of the lens is:
(a) 15 cm (b) 20 cm (c) 30cm (d) 10cm
A magnifying glass is to be used at the fixed
object distance of 2 cm. If it is to produce an erect
image magnified 5 times, its focal length is
(a) 2.5 cm
(b) -2.5 cm
(c) 5.0cm
(d) none of these
Two thin lenses are in contact and the focal length
of the combination is 80 cm. If the focal length of
one of the lenses is 20 cm, the power of the other
lens is:
(a) 1.66 (b) 4.00 (c) -1.00 (d) -3.75
A convex lens of power + 6 is placed in contact
with a concave tens of power – 4. What is the
nature and focal length of the combination?
(a) Concave, 25 cm
(b) Convex, 50 cm
(c) Concave, 20 cm
(d) Convex, 100 cm
22. An equiconvex glass lens (a) has a focal length f
and power P. It is cut into two symmetrical halves
(b) by a plane containing the principal axis. The
two pieces are recombined as shown in Fig (c).
The
power of
new
combina
tion is:
(a) P
(b) P/2
(c) 2P
(d) zero
23. Two thin convex lenses of focal lengths 20 cm and
5 cm, respectively, are placed at a distance d. If a
parallel beam incident on the first lens emerges as
a parallel beam from the second lens, then the
value of d is:
(a) 5 cm (b) 15 cm (c) 20cm (d) 25cm
24. Focal length of a lens for red colour is:
(a) same as that for violet
(b) greater than that for violet
(c) lesser than that of violet
(d) none of the above
25. A thin convex lens of crown glass ( = 1.5) has a
power of 1. Another convex lens with the same
radii of curvature and made up of a glass material
with refractive index 1.6 will have a power of:
(a) 1.2
(b) -0.9 (c) -0.8 (d) -1.06
26. A lamp is placed 6.0 m from a wall. On putting a
lens between the lamp and the wall at a distance of
1.2 m from the lamp, a real image of the lamp is
formed on the wall. The magnification of the
image is:
(a) 3
(b) 4
(c) 5
(d) 6
27. A plano-convex lens of focal length 20 cm
silvered at the plane surface will behave as
convergent mirror of focal length:
(a) 20 cm (b) 30 cm (c) 40cm (d) 10cm
28. A real image is formed by a convex lens. If we put
it in contact with a concave lens and the
combination again forms a real image, which of
the following is true for the new image from the
combination?
(a) Shifts towards the lens system
(b) Shifts away from the lens system
(c) Remains at the original position
(d) No image is formed
29. A concave lens of focal length 20 cm placed in
contact with a plane mirror acts as a:
(a) convex mirror of focal length 10 cm
(b) concave mirror of focal length 40 cm
(c) concave mirror of focal length 60 cm
(d) concave mirror of focal length 10 cm
Nishant Gupta, D-122, Prashant vihar, Rohini, Delhi-85
Contact: 9953168795, 9268789880
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30. A symmetrical double convex lens is cut in two
equal parts by a plane containing the principal
axis. If the power of the original lens was 4 , the
power of a divided lens will be:
(a) 2
(b) 3
(c) 4
(d) 5
31. A convex lens of focal length 20 cm is cut into
two equal parts so as to obtain two plano-convex
lenses as shown in figure, The two parts are then
put in contact as shown in figure. What is the focal
length
of
the
combination?
(a) Zero
(b) 5 cm
(c) 10 cm
(d) 20 cm
32. In the figure given below there are two convex
lenses L1 and L2 having focal lengths F1 and F2
respectively. The distance between L1 and L2 will
be:
(a) F1
(b) F2
(c) F1 + F2
(d) F1 – F2
33. fB and fR are the focal lengths of a convex lens for
blue and red light respectively and FB and FR are
the focal lengths of a concave lens for blue and red
light respectively. We must then have:
(a) fB < fR and FB < FR (b) fB < fR and FB > FR
(b) fB > fR and FB > FR (d) fB > fR and FB < FR
ANSWERS
1b ,2d ,3b ,4d ,5c ,6c ,7b ,8b ,9d ,10a ,11c
,12b ,13d ,14b ,15b ,16c ,17d ,18c ,19a ,20d
,21b ,22d ,23d ,24b ,25a ,26b ,27d ,28b ,29a
,30c ,31d ,32c ,33a
Nishant Gupta, D-122, Prashant vihar, Rohini, Delhi-85
Contact: 9953168795, 9268789880
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